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Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.


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TL;DR: This article describes a time-domain finite-difference algorithm for solving Maxwell's equations in generalized nonorthogonal coordinates that is similar to conventional leapfrog-differencing schemes, but now an additional leapfrogging between covariant and contravariant field representations becomes necessary.
Abstract: This article describes a time-domain finite-difference algorithm for solving Maxwell's equations in generalized nonorthogonal coordinates. We believe this approach would be most useful for applications where a uniform, uncurved, but oblique, meshing scheme could be applied in lieu of staircasing. This algorithm is similar to conventional leapfrog-differencing schemes, but now an additional leapfrogging between covariant and contravariant field representations becomes necessary.

282 citations

Journal ArticleDOI
TL;DR: In this paper, an investigation into the two-dimensional cure simulation of thick thermosetting composites is presented, where temperature and degree of cure distributions within arbitrary cross-sectional geometries are predicted as a function of the autoclave temperature history.
Abstract: An investigation into the two-dimensional cure simulation of thick thermosetting composites is presented. Temperature and degree of cure distributions within arbitrary cross-sectional geometries are predicted as a function of the autoclave temperature history. The heat conduction equation for two-dimensional, transient anisotropic heat transfer is coupled to the cure kinetics of the thermosetting composite material. A heat generation term, expressed as a function of cure rate and the total heat of reaction, is introduced to account for the heat liberated during the curing process. A generalized boundary condition formulation is employed, enabling arbitrary temperature boundary conditions to be enforced straightforwardly. An incremental, transient finite difference solution scheme is implemented to solve the pertinent governing equations and boundary conditions. The boundary-fitted coordinate system (BFCS) transformation technique is combined with the Alternating Direction Explicit (ADE) finite difference ...

279 citations

Journal ArticleDOI
TL;DR: In this article, a discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids, where the governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model.
Abstract: A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplyfying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

279 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a numerical method for computing the motion of complex solid/liquid boundaries in crystal growth, which includes physical effects such as crystalline anisotropy, surface tension, molecular kinetics and undercooling.

279 citations

Journal ArticleDOI
TL;DR: In this article, an approximate expression for the history force on a spherical bubble is proposed for finite Reynolds number, Re. Satisfactory agreement is observed between the presently proposed history force and the numerical solution.
Abstract: An approximate expression for the history force on a spherical bubble is proposed for finite Reynolds number, Re. At small time, the history‐force kernel is a constant, which decreases with increasing Re, and the kernel decays as t−2 for large time. For an impulsively started flow over a bubble, accurate finite difference results show that the history force on the bubble decays as t−2 at large time. Satisfactory agreement is observed between the presently proposed history force and the numerical solution.

278 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022411
2021722
2020679
2019678
2018708